Over the past decades, although stochastic system control has been studied intensively within the field of control engineering, all the modelling and control strategies developed so far have concentrated on the performance of one or two output properties of the system, such as minimum-variance control or mean-value control. The general assumption used in the formulation of modelling and control strategies is that the distribution of the random signals involved is Gaussian. In this book, a set of new approaches for the control of the output probability density function of stochastic dynamic systems (those subjected to any bounded random inputs), has been developed. In this context, the purpose of control system design becomes the selection of a control signal that makes the shape of the system output's p.d.f. as close as possible to a given distribution. The book contains material on the subjects of:

. Control of single-input single-output and multiple-input multiple-output stochastic systems.

. Stable adaptive control of stochastic distributions.

. Model reference adaptive control.

. Control of nonlinear dynamic stochastic systems.

. Condition monitoring of bounded stochastic distributions.

. Control algorithm design.

. Singular stochastic systems.

A new representation of dynamic stochastic systems is produced by using B-spline functions to describe the output p.d.f.

Inhalt

1 Preliminaries.- 1.1 Introduction.- 1.2 An example: flocculation model.- 1.3 The aim of the new development.- 1.4 The structure of the book.- 1.5 Random variables and stochastic processes.- 1.5.1 Random variables and their distribution functions.- 1.5.2 Mean and variance.- 1.5.3 Random vector.- 1.5.4 Conditional mean.- 1.6 Stochastic processes.- 1.7 Some typical distributions.- 1.7.1 Gaussian distribution.- 1.7.2 Uniform distribution.- 1.7.3 ? distribution.- 1.8 Conclusions.- 2 Control of SISO Stochastic Systems: A Fundamental Control Law.- 2.1 Introduction.- 2.2 Preliminaries on B-splines artificial neural networks.- 2.3 Model representation.- 2.3.1 Static models.- 2.3.2 Dynamic models.- 2.4 System modelling and parameter estimation.- 2.4.1 Modelling of static systems.- 2.4.2 Modelling of linear dynamic systems.- 2.5 Control algorithm design.- 2.5.1 Control algorithm for static systems.- 2.5.2 Control algorithm for linear dynamic systems.- 2.5.3 Constraints on input energy for dynamic systems.- 2.6 Discussions.- 2.6.1 Adaptive control.- 2.6.2 Modelling and control of time delay systems.- 2.6.3 On-line measurement of Vk.- 2.6.4 Controllability, observability and stability.- 2.7 Examples.- 2.7.1 Static system modelling.- 2.7.2 A design example for dynamic systems.- 2.8 Conclusions.- 3 Control of MIMO Stochastic Systems: Robustness and Stability.- 3.1 Introductionx.- 3.2 Model representation.- 3.2.1 State space form.- 3.2.2 The input-output form.- 3.3 The controller using V(k).- 3.3.1 Measurement of V(k).- 3.3.2 Feedback control using V(k).- 3.3.3 Stability issues.- 3.4 The controller using f(y, U(k)).- 3.4.1 The formulation of control algorithm.- 3.4.2 Stability issues.- 3.5 An illustrative example.- 3.5.1 Control algorithm design.- 3.5.2 Simulation results.- 3.6 Conclusions and discussions.- 4 Realization of Perfect Tracking.- 4.1 Introduction.- 4.2 Preliminaries and model representation.- 4.3 Main result.- 4.4 Simulation results.- 4.4.1 Controller design.- 4.4.2 Simulation results.- 4.5 An LQR based algorithm.- 4.6 Conclusions.- 5 Stable Adaptive Control of Stochastic Distributions.- 5.1 Introduction.- 5.2 Model representation.- 5.3 On-line estimation and its convergence.- 5.4 Adaptive control algorithm design.- 5.5 Stability analysis.- 5.6 A simulated example.- 5.7 Conclusions.- 6 Model Reference Adaptive Control.- 6.1 Introduction.- 6.2 Model representation.- 6.3 An adaptive controller design.- 6.3.1 Construction of the reference model.- 6.3.2 Construction of error dynamics.- 6.4 Adaptive tuning rules for K(t) and Q(t).- 6.5 Robust adaptive control scheme.- 6.5.1 Control scheme when ?(t) ? 0.- 6.5.2 Control scheme when both e0 and ? are present.- 6.6 A case study.- 6.7 Conclusions and discussions.- 7 Control of Nonlinear Stochastic Systems.- 7.1 Introduction.- 7.2 Model representation.- 7.3 Control algorithm design.- 7.4 Stability issues.- 7.5 A neural network approach.- 7.5.1 Training of the neural networks.- 7.5.2 A linearised control algorithm.- 7.6 Two examples.- 7.7 Calculation of ?.- 7.8 Conclusions.- 8 Application to Fault Detection.- 8.1 Introduction.- 8.2 Model representation.- 8.3 Fault detection.- 8.3.1 Fault detection for static systems.- 8.3.2 Dynamic systems.- 8.3.3 Fault detection signal.- 8.4 An adaptive diagnostic observer.- 8.5 Discussions.- 8.6 An identification based FDD.- 8.7 Fault diagnosis.- 8.7.1 The algorithm.- 8.7.2 An applicability study.- 8.8 Discussions and conclusions.- 9 Advanced Topics.- 9.1 Introduction.- 9.2 Square root models.- 9.3 Control algorithm design.- 9.3.1 Finding weights from ?(y, u(k)).- 9.3.2 The control algorithm.- 9.4 Simulations.- 9.5 Continuous-time models.- 9.6 The control algorithm.- 9.7 Control of the mean and variance.- 9.7.1 The control of output mean value.- 9.7.2 The control of output variance.- 9.8 Singular stochastic systems.- 9.8.1 Model representation.- 9.8.2 Control algorithm design.- 9.9 Pseudo ARMAX systems.- 9.10 Filtering issues.- 9.11 Conclusions.- References.